Again, Mozina rants & talks trash, but has nothing intelligent to say. The ability of magnetic fields to inhibit convective heat transport is well known & well established, and indeed fairly obvious: Plasma does not cross magnetic field lines. The physics is well described in any number of sources, e.g.,
Solar Astrophysics by Peter Foukal (Wiley-VCH, 2004 2nd revised edition), section 8.2.2 "Why Spots Are Cool" ...
The most promising explanation of the spots coolness, and the fate of the missing energy, seems to lie in the blocking of convection by intense vertical magnetic fields. This explanation was first put forward by Biermann in 1941, and some recent evidence tends to strengthen the argument. The basic idea is that the horizontal motions of overturning convection are inhibited by the magnetic volume force jxB in the presence of a strong vertical magnetic field. ... In this explanation of the spot coolness, an equilibrium would be reached in which the convective heat flux blocked below the spot would simply flow around it ...
Solar Astrophysics, Peter Foukal, 2nd ed. 2004, page 250. See the book for complete details.